The average of the least primitive root modulo
D. Burgess (1971)
Acta Arithmetica
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D. Burgess (1971)
Acta Arithmetica
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J. Mikusiński (1953)
Studia Mathematica
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H. Kesten (1964)
Acta Arithmetica
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Mordechay B. Levin (2001)
Journal de théorie des nombres de Bordeaux
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Let be integers, and let be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences in -dimensional unit cube . We also find a lower bound of the discrepancy (up to a logarithmic factor) of the sequence (Korobov’s problem).
Nobushige Kurokawa, Masato Wakayama (2005)
Rendiconti del Seminario Matematico della Università di Padova
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C. Hooley (1963)
Acta Arithmetica
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Calixto Calderón (1973)
Studia Mathematica
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P. Ney, S. Wainger (1972)
Studia Mathematica
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W. K. A. Loh (1996)
Acta Arithmetica
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J.-L. Nicolas, A. Sárközy (2000)
Journal de théorie des nombres de Bordeaux
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Let denote the number of partitions of into parts, each of which is at least . By applying the saddle point method to the generating series, an asymptotic estimate is given for , which holds for , and .
Chang-Pao Chen (1994)
Studia Mathematica
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We prove that if as max(|j|,|k|) → ∞, and , then f(x,y)ϕ(x)ψ(y) ∈ L¹(T²) and as min(m,n) → ∞, where f(x,y) is the limiting function of the rectangular partial sums , (ϕ,θ) and (ψ,ϑ) are pairs of type I. A generalization of this result concerning L¹-convergence is also established. Extensions of these results to double series of orthogonal functions are also considered. These results can be extended to n-dimensional case. The aforementioned results generalize work of Balashov [1],...